cva {ebci}

Compute average coverage critical value under moment constraints.

Description

Computes the critical value cva_{\alpha}(m_{2}, \kappa) from Armstrong, Kolesár, and Plagborg-Møller (2020).

Usage

cva(m2, kappa = Inf, alpha = 0.05, check = TRUE)

Arguments

m2

Bound on second moment of the normalized bias, m_{2}

kappa

Bound on the kurtosis of the normalized bias, \kappa

alpha

Determines confidence level, 1-\alpha.

check

If TRUE, verify accuracy of the solution by checking that the implied least favorable distribution satisfies the m2 and kappa constraints and yields the same non-coverage rate. If this fails (perhaps due to numerical accuracy issues), solve a finite-grid approximation (by discretizing the support of the normalized bias) to the primal linear programming problem, and check that it agrees with the dual solution.

Value

Returns a list with 4 components:

cv

Critical value for constructing two-sided confidence intervals.

alpha

The argument alpha.

x

Support points for the least favorable distribution for the squared normalized bias, b^2.

p

Probabilities associated with the support points.

References

Armstrong, Timothy B., Kolesár, Michal, and Plagborg-Møller, Mikkel (2020): Robust Empirical Bayes Confidence Intervals, https://arxiv.org/abs/2004.03448

Examples

# Usual critical value
cva(m2=0, kappa=Inf, alpha=0.05)
# Larger critical value that takes bias into account. Only uses second moment
# constraint on normalized bias.
cva(m2=4, kappa=Inf, alpha=0.05)
# Add a constraint on kurtosis. This tightens the critical value.
cva(m2=4, kappa=3, alpha=0.05)